/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution
{
public:
    int widthOfBinaryTree(TreeNode* root)
    {
        vector<pair<TreeNode*, unsigned int>> q;
        q.push_back({ root, 1 });
        unsigned int ret = 0;

        while (q.size())
        {
            auto& [x1, y1] = q[0];
            auto& [x2, y2] = q.back();

            ret = max(ret, y2 - y1 + 1);
            vector<pair<TreeNode*, unsigned int>> tmp;
            for (auto& [x, y] : q)
            {
                if (x->left) tmp.push_back({ x->left, 2 * y });
                if (x->right) tmp.push_back({ x->right, 2 * y + 1 });
            }
            q = tmp;
        }
        return ret;
    }
};